CAS Exam 9 Spring 2019, Question 14
Study guide: Exam 9
An insurer has an opportunity to write a new program with the following characteristics:
- Premium of $1,000 collected and earned at time 0
- Expected loss of $650 paid at time 2
- Insurer cost of capital of 9%
- Expenses of $300, excluding commission, are incurred and paid at time 0
- The commission is incurred and paid at time 0
- Loss reserves are established at time 0 and there are no unearned premium reserves
- Surplus and reserves will be invested in a 2-year risk free zero coupon bond with a yield of 4%
- The required reserve to surplus ratio is 1.5
- There are no taxes
Part a (1.25 points)
Determine the maximum commission as a percentage of premium so that the insurer's Internal Rate of Return (IRR) matches its cost of capital.
Part b (0.5 points)
If the commission is fixed and expected losses are increased, describe the effects on projected investment income, and the IRR.
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